CDD pole effects on the P33 channel of the Chew–Low model without crossing

Abstract

To better understand the role of CDD poles in modern field theories, we investigate the effects of CDD poles on the [Formula: see text] channel in [Formula: see text] scattering. We use the non-crossing Chew–Low model for this investigation. The Chew–Low model is the simplest phenomenological model of [Formula: see text] scattering. In the no crossing limit, the [Formula: see text] channel can be easily solved and displays the predominate [Formula: see text] resonance. It has been shown that the denominator function, used in the [Formula: see text] method of solution, is a generalized R-function. Our research centers on two investigations. The first is whether one can readily associate a CDD pole with the [Formula: see text] resonance. We find that one cannot, since the CDD pole forces the phases to disagree with the experimental values. The second investigation is into the nature of the redundant solutions one can generate by adding CDD pole to the denominator function. We find that the solutions with the added CDD pole cannot reproduce the phases of the original Chew–Low Model at low energies. Thus, there are no redundant solutions to this model. These results are contrary to what is generally assumed. We question the use of adding a CDD pole to produce resonances and the ideal that adding such poles do not effect the low energy phases.